Figure 1. Map of the study area. (a) Köppen-Geiger climate classification of the eastern Mediterranean (Atlas of Israel, 2011), weather research and forecasting (WRF) model domains (D1-D3; Sect. 2.3), and the range of the weather radar used for the identification of events (Sect. 2.2). (b) Mean annual rainfall based on 1960-1990 interpolated rain gauge data (Enzel et al., 2003), the innermost model domain, and the weather radar range. Green and yellow colors, corresponding to drier and wetter than 200 mm yr-1, respectively, roughly mark the extent of the desert and Mediterranean climate regions. SND = Sinai-Negev Desert, LM = Lebanon Mountains.
2.2 HPEs Identification
A collection of carefully selected HPEs was used in this study (Table S1 in the Supporting Information) following Armon et al. (2020) and described here briefly. It consists of 41 HPEs identified based on their magnitude compared to a 24-year rainfall climatology from physically-corrected and gauge-adjusted weather radar rainfall data (Marra & Morin, 2015; Fig. 1b). A HPE was identified when at least a thousand 1-km2 radar pixels exhibited a rain amount greater than the local 99.5th quantile of the non-zero amounts for multiple durations, thus revealing events which can be considered locally intense. To have a good representation of both short- and long-duration HPEs, this process was repeated for durations of 1-72 h. Events identified as a HPE for more than one duration were merged (Table S1). Return levels of the 99.5th quantile thresholds are roughly 2-10 years. Events were separated by at least 24 h with less than 100 pixels displaying rainfall of more than 0.1 mm, and they span 3.4 ± 1.6 d (mean and standard deviation). This collection of HPEs represents a large variance of synoptic conditions, associated with both MCs (35 events) and ARSTs (six events). A detailed description of the collection of events and their rainfall characteristics is given in Armon et al. (2020).
2.3 WRF Simulations
Each of the 41 HPEs was simulated twice, using version 3.9.1.1 of the weather research and forecasting (WRF) model, at a convection permitting resolution. The first simulation of each event represents the historic conditions during the storm (near the end of the 20thcentury; sect. 2.3.1). Results of these simulations were previously published (Armon et al., 2020). The second simulation represents a hypothetic storyline in which the same HPE hits the area by the end of the 21st century, when global warming conditions at a representative concentration pathway (RCP) 8.5 prevail in the region (sect. 2.3.2).
2.3.1 Simulation of Historic HPEs
Simulation of historic HPEs was conducted at a configuration suitable for a skillful representation of rainfall patterns in the eastern Mediterranean (Armon et al., 2020; Romine et al., 2013; Rostkier-Edelstein et al., 2014; Schwartz et al., 2015). This configuration includes three two-way nested domains (Fig. 1a; Table S2) in which the innermost domain is simulated at a very high spatial and temporal resolution (1 km2, 4-8 s). Convective parametrization was used only in the two outer nests, while in the inner nest the resolution is high enough to explicitly represent convection (e.g. Prein et al., 2015). Further details are described in Table S2 and in Armon et al. (2020).
Initial and boundary conditions for the historic simulations are 6-hourly ERA-Interim reanalysis data, at 60 vertical layers with a T255 spectral spatial resolution (~80 km) (Dee et al., 2011). HPEs were simulated starting 24 h before the beginning of the observed rainfall (rounded down to the previous 6 h) and lasted until the end of the HPE (rounded to the following 6 h). The 24 h period before the event is considered a spinup phase, for which we discard the rain fields. This duration is considered long enough to correct spatial heterogeneities arising from the initial conditions (Gómez-Navarro et al., 2019; Picard & Mass, 2017; Warner, 2011: pp 215-216), which is crucial in correcting non-physical properties of the atmosphere, expected to be present in the PGW simulations because of the usage of ensemble mean fields (Shepherd, 2019; Tebaldi & Knutti, 2007) (Sect. 2.3.2). Precipitation outputs for the innermost domain were saved at 10 min intervals.
As was shown by Armon et al. (2020), the total precipitation during most of the HPEs reproduces the structure, location, and the seasonal change of the precipitation’s center-of-mass of radar-observed precipitation, albeit with a positive bias. Given that HPEs in the region are characterized by small spatiotemporal scale rain-cells, it is important to note the model’s skill is particularly good at its “raw” (1 km2) resolution for total rain amounts of <25 mm, however, for larger amounts a skillful representation must include a spatial averaging of at least a few tens of square kilometers. The model also well represents areal mean rainfall amounts, for various durations, which are crucial drivers of the hydrological response to precipitation. MC-type HPEs are better simulated compared to ARSTs, which are in general shorter and more local in nature.
2.3.2 Simulation of “Future” HPEs
To simulate the occurrence of the same HPEs in the future we used the “pseudo global warming” (PGW) methodology (Kawase et al., 2009; Rasmussen et al., 2011; Schär et al., 1996). Each of the simulated HPEs was forced with the same input data as the historic events (Sect. 2.3.1) after adding the signal of climate change to the following input variables: surface pressure, skin temperature (including sea surface temperature), and 3D fields of temperature, wind, and specific humidity. In contrast to homogeneous changes common in the surrogate climate-change methodology (Keller et al., 2018; Schär et al., 1996), 3D spatial heterogeneity in the altered fields used in PGW experiments allows for representation of non-uniform spatial response to global warming (e.g., Rasmussen et al., 2011).
The changes applied over the initial and boundary conditions, for each pixel and timestep (denoted hereon as \(\Delta\)), were derived from the monthly values (Oct-Apr) of the ensemble mean of 29 models of the Coupled Model Intercomparison Project phase 5 (CMIP5; Table S3) (K. E. Taylor et al., 2012). They were based on the difference in the corresponding parameter values for the end of the 21stcentury and the end of the 20th century under an RCP 8.5 scenario, as follows:
\(\Delta X_{j}=\left.\ \overset{}{X_{j}}\right|_{\mathbf{2074-2099}}^{29\ models}-\left.\ \overset{}{X_{j}}\right|_{\mathbf{1979-2004}}^{29\ models}\), (1)
where \(X\) is a specified meteorological variable, defined for the particular month (\(j\)) of the HPE occurrence. The double overbar represents the mean of this parameter over the future (2074 to 2099) or historic (1979 to 2004) periods, averaged among the 29 CMIP5 models.\(\Delta\) fields were linearly interpolated into a common grid, similar to the ERA-Interim horizontal grid (T255) and consisting of 42 levels in the vertical (model top = 10 hPa) for the 3D fields, over the entirety of the outermost domain. The changes applied represent a major warming of the region over the whole troposphere, but specifically over its upper levels. Surface temperature increases on average by 4.3°C. Alongside the warming, is a decrease in the zonal component of wind and an increase of the sea level pressure in the central Mediterranean, as detailed in the Supporting Information Text S1 and Fig S1.
2.4 Analyzed Rainfall Parameters and Statistical Methods
The parameters examined here are based on the 10-min rainfall fields from the innermost domain of both the historic and the “future” (PGW) simulations. Rainfall parameters from the historic and future simulations were compared both through their entire distribution across all events and through an event-based paired comparison (historic-future). To enable comparison between events of different magnitudes, in many instances we normalize the quantity examined to its historic value:\(100\times\frac{\overset{\overline{}}{\text{futur}e_{i}\ \ historic_{i}}}{\overset{\overline{}}{\text{histori}c_{i}}}\), where \(i\) indicates a specific event for which “future” and “historic” quantities are spatially averaged.
The following rainfall parameters were considered for each event:
(1) Rainfall accumulation for each pixel.
(2) Areal mean rainfall accumulation, which is the average of (1) over the region of interest.
(3) Factors affecting areal mean rainfall accumulation: the value in (2) above can be obtained by integrating rain rates over all rainy pixels and timesteps and divide by the area of the region. Therefore, it is possible to consider three factors affecting the areal mean accumulation:
  1. The mean conditional rain rate is the average of rain rates >0.1 mm h-1 over all timesteps and pixels.
  2. The duration of the events is defined here as the time it took the central 90% of rainfall mass to precipitate.
  3. The rain area of the event is the time-average of the area covered by 10-min rain rates >0.1 mm h-1 along the event. We also examine the rain area for higher rain rate thresholds in the range of 0.5-100 mm h-1.
(4) Maximal rain rates for durations of 10, 20 and 30 min, 1, 3, 6, 12 and 24 h for each pixel. To diminish the effect of single outlier pixels, the rain field is first smoothed spatially using a 3X3 pixel moving average window.
(5) Regionally maximal rain rates for the same durations as in (4), which are taken as the maximal value from (4) over all pixels in the region.
The analyses above were evaluated both over the entire study region and over four sub-regions (Fig. 1b). These are the Mediterranean Sea area, the land area, and a division of the latter to the area north to the 200 mm isohyet roughly corresponding to the Mediterranean climate zone, and the area south of the 200 mm isohyet roughly corresponding to the desert climate zone.
To analyze changes in the spatial structure of precipitation we compared the spatial autocorrelation structure of the 10-min rain fields whenever these were considered as having convective elements, following Marra and Morin (2018). Convective elements are defined here as spatially connected regions of area ≥3 km2 with rain rates >10 mm h-1 that include at least one pixel with rain rate >25 mm h-1. Following Peleg et al. (2013), the spatial autocorrelation was calculated through fitting a three-parameter exponential function to the 2D spatial autocorrelation field (e.g., Nerini et al., 2017) of each of the convective rain fields as in Eq. 2:
\(r\left(h\right)=ae^{-\left(\frac{h}{b}\right)^{c}}\), (2)
where h is the lag distance, b , termed the correlation distance, is the distance at which the correlation decreases to\(r=\text{ae}^{-1}\), a is the nugget (interception) parameter and c is the shape parameter. For each event, the representative parameters of Eq. (2) are the intra-event medians over all convective rain fields. The comparison of the autocorrelation structure between historic and future events is based on the inter-event medians of these representative parameters.
Statistical significance of the changes in pixel- based parameters is determined through the paired t-test with 5% significance level. For event-based parameters, statistical significance is declared if both paired t-test and paired Wilcoxon signed-rank tests are statistically significant at the 5% level.
3 Results
To have a better understanding of the changes between “future” (PGW) and historic simulations, we first present an examination of the first HPE in our collection, which exhibits many of the features observed throughout the events. It is followed by the results obtained throughout the HPEs collection.
3.1 Case Study #1
The first HPE in our collection (2-5 Nov 1991) is characterized by the passage of a MC, triggering numerous rain cells crossing the region with a general SW-NE track. These rain cells contributed >100 mm of accumulated rainfall mainly to the north coast and mountainous areas of the study region (Fig. 2a, Movie S1). The areal average rainfall accumulation simulated over the entire domain for the historic event is 21.9 mm. Compared to the historic event, the future event exhibits a pronounced (-20%) decrease in precipitation with areal average rainfall accumulation summing to 17.5 mm (Fig. 2b-c). The decrease is more pronounced over the land area (-28%) compared to the sea area (-16%), and is similar between the desert and Mediterranean regions of the land area (-29% and -27%, respectively).
In contrast to the decrease in total rain amounts, short duration (10-min) rain rates reveal a more complicated pattern (Fig. 2d). When considering the distribution of all 10-min timesteps and pixels, including those with no-rain (i.e., unconditional rain rates), most of the distribution presents decreased rain rates and only the uppermost quantiles (>99.75%) of future rain rates increase compared to the historic ones. For example, the 99.99% quantile (corresponding to ~1.4 104 pixel-timesteps values of 10-min rain rates), is increased by 21% (from 77 mm h-1 to 93 mm h-1). However, the decrease in most of the unconditional rain rate quantiles is very much affected by the change in the spatiotemporal coverage of the event, namely the wet-frequency. Conversely, considering the distribution of the rainy pixels and timesteps, i.e., the conditional 10-min rain rate, quantiles of the future HPE are increasing throughout the distribution (Fig. 2d inset). The mean value of the conditional rain rate increases from 2.64 mm h-1 for the historic event to 3.43 mm h-1 for the future one (+30%).
In addition to the mean conditional rain rate, two other factors affect the areal mean rainfall (Sect. 2.4), the duration and the rain area (Fig. 2e). The duration of the event (Fig. S2a) decreased from 2440 min to 1850 min (-24%) between the historic and future simulations. This reduction reflects a delayed start of the “core” of the rainfall during the passage of the MC, and an earlier termination (Movie S1). The rain area (Fig. 2e) exhibits a major contraction (-38%) between the historic and future simulations, from 31.9 103km2 (10.5% of the study region) to 19.7 103 km2 (6.5%) in historic and future simulations, respectively. This major decrease in rain area reflects the decrease in the area of precipitating rain cells, seen clearly in Movie S1, as well as in their number. However, it is important to note that we leave for future work a quantitative assessment or tracking of individual rain cells (e.g., Belachsen et al., 2017; Peleg & Morin, 2012). Nevertheless, we did compute the spatial autocorrelation of convective rainfall (Sect. 2.4). The spatial autocorrelation distance is 7 km and 5 km, respectively for the historic and future events (Fig. S2b). In addition, the number of 10-min convective timesteps decreases by 5.1% (from 429 to 407).
In summary, this case study of the first HPE in our collection indicates that, moving from historic to future climates, areal mean rainfall accumulation decreases whereas conditional 10-min rain rates increase. This opposing behavior is caused by the decrease in the duration of the rainfall and even a greater decrease in the rain area, where the latter is probably due to the reduction in the area of precipitating rain cells and possibly in their number. The decrease in duration and in rain area, which means a decrease in wet-frequency, leads also to a decrease in almost all quantiles (except the uppermost ones) of the unconditional rain rate distribution, while the conditional rain rate distribution presents an increase in all quantiles.